The country’s largest gay-rights group today demanded an apology from David Letterman, for making what it called “inappropriate and incendiary remarks” regarding President Obama’s appointment of a transgender woman to the Commerce Department.

In his monologue Tuesday, Letterman remarked that Amanda Simpson, a transgender woman, had been appointed to work in the Commerce Department’s Bureau of Industry and Security, where she will monitor the export of military technology.

As a photograph of Simpson was shown, announcer Alan Kalter shouted, “What? Amanda? Amanda used to be a dude?”

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“Oh my God!” he shouted, before running off stage, with audience laughing.

In a letter to Letterman and CBS Entertainment President Nina Tassler, Human Rights Campaign called the bit “inappropriate and incendiary” and said it reflected “transphobia,” a fear or hatred of transgender people.

“Your skit affirmed and encouraged a prejudice against transgender Americans that keeps many from finding jobs, housing, and enjoying freedoms you and your writers take for granted every day,” HRC’s Allyson Robinson wrote in the letter.